1. Technical Field
The present invention relates in general to interferometry and, in particular, to the stabilization and demodulation of an interferometer at quadrature.
2. Description of the Related Art
An interferometer can be utilized to measure the small displacement amplitude of a vibrating target based upon the pattern formed by interfering two beams of light. Interferometry finds use, for example, in acoustic sensing, transducer calibration and microelectromechanical systems (MEMS) characterization.
FIG. 1 illustrates a conventional fiber-optic interferometer in the Michelson configuration. As shown, laser light emitted from a Hexe2x80x94Ne laser 10 is split into a signal arm beam 12 and a reference arm beam 14 by a fiber-optic coupler 16. Fiber-optic coupler 16 transmits reference arm beam 14 via fiber to a reference mirror 20, which reflects reference arm beam 14 back to fiber-optic coupler 16. Signal arm beam 12 is similarly transmitted via fiber to a target 24, which reflects signal arm beam 12 back to fiber-optic coupler 16. Reference mirror 20 is driven by a piezoelectric transducer (PZT) 22 to produce a sinusoidal variation in the optical path length of the reference arm having a known amplitude and frequency. Target 24 similarly vibrates sinusoidally at a known frequency and unknown amplitude.
Fiber-optic coupler 16 combines signal and reference arm beams 12 and 14 to form a combined beam 26 that exhibits an interference pattern. To maximize fringe contrast in the interference pattern, a polarization controller 18 may be employed in one of the reference or signal arms to match the polarization of reference and signal arm beams 12 and 14. Combined beam 26 is then transmitted to a photodetector 28, which produces an electrical signal indicative of the incident optical power. The optical power (PO), which varies as the optical path length difference between the reference and signal arms, has the form
POxe2x88x9dRe{EroEto*}cos("PHgr"+2kxcex4),xe2x80x83xe2x80x83(1) 
where
Ero=complex electric field amplitude of the reference arm beam,
Eto*=complex conjugate of electric field amplitude of the signal arm beam,
"PHgr"=static optical path length difference between reference and signal arms;
k=propagation constant of light, and
xcex4=target displacement.
In practical systems, the reference and signal arms typically have unequal contributions to the total optical power incident upon photodetector 28. In such cases, the maximum measurement sensitivity (i.e., the greatest change in optical power for an incremental change in target amplitude) occurs when "PHgr", the optical path length difference between the reference and signal arms, is equal to (xcfx80/2)xc2x1xcfx80n, where n is an integer. This condition, which is known as quadrature, is difficult to maintain in practice because vibrations and temperature and humidity-induced variations in k, the propagation constant, cause "PHgr" to drift from quadrature over time.
Accordingly, the present invention recognizes that it would be useful and desirable to provide a method and system for stabilizing an interferometer at quadrature.
The present invention provides an improved method and system for stabilizing and demodulating an interferometer at quadrature.
According to a preferred embodiment of the present invention, an interferometer control system receives from an interferometer a signal indicative of optical power of the interferometer. In response to receipt of the signal, the interferometer control system determines an optical path length correction required to stabilize the interferometer at quadrature utilizing signal amplitudes appearing at multiple harmonics of the signal. In a particularly preferred embodiment, the signal amplitudes are calculated utilizing the Goertzel algorithm, a computationally efficient discrete Fourier transform. The interferometer control system then outputs an error signal indicative of the optical path length correction. In a preferred embodiment, the error signal forms the DC component of a composite stabilization signal, whose AC component is the reference modulation signal utilized to excite a transducer to modulate the optical path length of the interferometer. With the interferometer stabilized at quadrature, the interferometer control system determines a first signal amplitude of a particular harmonic without target oscillation and a second signal amplitude of the same harmonic with target oscillation. Based upon the relative magnitudes of the first and second signal amplitudes, the interferometer control system determines a solution set for the displacement amplitude of the interferometer target. Any ambiguity in the displacement amplitude can then be eliminated utilizing additional information gained from the signal amplitude present at a harmonic of a target oscillation frequency.
Additional objects, features, and advantages of the present invention will become apparent from the following detailed written description.